Optimal non-asymptotic concentration of centered empirical relative entropy in the high-dimensional regime

Yanpeng Li; Boping Tian

doi:10.1016/j.spl.2023.109803

Optimal non-asymptotic concentration of centered empirical relative entropy in the high-dimensional regime

Yanpeng Li^*
, Boping Tian

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

This document establishes the optimal non-asymptotic concentration of the Kullback–Leibler divergence between the empirical distribution and the true distribution around its mean in the regime of K≫n, where K and n are the alphabet size and sample size, respectively.

Original language	English
Article number	109803
Journal	Statistics and Probability Letters
Volume	197
DOIs	https://doi.org/10.1016/j.spl.2023.109803
State	Published - Jun 2023
Externally published	Yes

Keywords

Empirical distribution
Kullback–Leibler divergence
Non-asymptotic
Plug-in entropy estimator

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10.1016/j.spl.2023.109803

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title = "Optimal non-asymptotic concentration of centered empirical relative entropy in the high-dimensional regime",

abstract = "This document establishes the optimal non-asymptotic concentration of the Kullback–Leibler divergence between the empirical distribution and the true distribution around its mean in the regime of K≫n, where K and n are the alphabet size and sample size, respectively.",

keywords = "Empirical distribution, Kullback–Leibler divergence, Non-asymptotic, Plug-in entropy estimator",

author = "Yanpeng Li and Boping Tian",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier B.V.",

year = "2023",

month = jun,

doi = "10.1016/j.spl.2023.109803",

language = "英语",

volume = "197",

journal = "Statistics and Probability Letters",

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publisher = "Elsevier B.V.",

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T1 - Optimal non-asymptotic concentration of centered empirical relative entropy in the high-dimensional regime

AU - Li, Yanpeng

AU - Tian, Boping

PY - 2023/6

Y1 - 2023/6

N2 - This document establishes the optimal non-asymptotic concentration of the Kullback–Leibler divergence between the empirical distribution and the true distribution around its mean in the regime of K≫n, where K and n are the alphabet size and sample size, respectively.

AB - This document establishes the optimal non-asymptotic concentration of the Kullback–Leibler divergence between the empirical distribution and the true distribution around its mean in the regime of K≫n, where K and n are the alphabet size and sample size, respectively.

KW - Empirical distribution

KW - Kullback–Leibler divergence

KW - Non-asymptotic

KW - Plug-in entropy estimator

UR - https://www.scopus.com/pages/publications/85148769352

U2 - 10.1016/j.spl.2023.109803

DO - 10.1016/j.spl.2023.109803

M3 - 文章

AN - SCOPUS:85148769352

SN - 0167-7152

VL - 197

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

M1 - 109803

ER -

Optimal non-asymptotic concentration of centered empirical relative entropy in the high-dimensional regime

Abstract

Keywords

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